In the first part I explain the classical construction of quasi-morphisms by Brooks, a connection between quasi-morphisms and stable commutator length of a group element, scl.

In the second part I discuss algebraic conditions for an element to have scl=0, and on the other hand, explain why negative curvature tends to imply scl>0. Combining them I give a precise condition for a mapping class to have scl >0 in terms Nielsen-Thurston classification. This is a joint work with Bestvina and Bromberg.